Multiple Linear Fitting, - HP 48gII User Manual

Example 3 – Test of significance for the linear regression.
hypothesis for the slope H
0, at the level of significance α = 0.05, for the linear fitting of Example 1.
The test statistic is t = (b -Β
0
The critical value of t, for ν = n – 2 = 3, and α/2 = 0.025, was
18.95.
obtained in Example 2, as t
t , we must reject the null hypothesis H
α
/2
= 0.05, for the linear fitting of Example 1.
Multiple linear fitting
Consider a data set of the form
x
1
x
11
x
12
x
13
.
.
x x
1,m-1
x
1,m
Suppose that we search for a data fitting of the form y = b
⋅x ⋅x
b + ... + b . You can obtain the least-square approximation to the
3 3 n n
values of the coefficients b = [b
matrix X:
_
1 x
11
1 x
12
1 x
13
. .
. .
1 x
1,m
_
: Β = 0, against the alternative hypothesis, H
0
)/(s /√S ) = (3.24-0)/(√0.18266666667/2.5) =
0 e xx
= t = 3.18244630528. Because, t
α
n-2, /2 3,0.025
: Β ≠ 0, at the level of significance α
1
x x ...
2 3
x x ...
21 31
x x ...
22 32
x x ...
32 33
. .
. . .
x ...
2,m-1 3,m-1
x x ...
2,m 3,m
b b b ... b
0 1 2 3
x x
21 31
x x
22 32
x x
32 33
. .
. .
x x
2,m 3,m
Test the null
x y
n
x y
n1 1
x y
n2 2
x y
n3 3
. .
. .
x y
n,m-1 m-1
x y
n,m m
⋅x
+ b + b
0 1 1 2
], by putting together the
n
_
... x
n1
... x
n2
... x
n3
.
. .
... x
n,m
_
Page 18-56
: Β ≠
1
>
0
⋅x
+
2